Almost cut short new hanging (7)
I believe the answer is:
curtain
'hanging' is the definition.
(thesaurus)
'almost cut short new' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'cut short' becomes 'curtail' (synonyms).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'curtail' with its last letter taken off is 'curtai'.
'curtai'+'n'='CURTAIN'
(Other definitions for curtain that I've seen before include "Hanging cloth" , "Cover for window etc" , "Hanging material screen" , "Fabric window covering" , "Window material" .)